stuart_1996
===========

B\. C\. Stuart, M\. D\. Feit, S\. Herman, A\. M\. Rubenchik, B\. W\. Shore and M\. D\. Perry, "Nanosecond\-to\-femtosecond laser\-induced breakdown in dielectrics", Phys\. Rev\. B 53, 1749 \(1996\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/stuart_1996.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/physrevb\.53\.1749 <https://doi.org/10.1103/physrevb.53.1749>`__

**Source kind:** measurement

**Recorded technique:** Front\-surface laser damage of polished dielectrics with a 1053\-nm Ti\:sapphire chirped\-pulse amplifier \(10 Hz\), compressed to 0\.4 ps \- 1 ns \(intensity FWHM\), and its second harmonic at 526 nm \(275 fs and longer, KD\*P doubler\); one point at 825 nm, 140 fs \(Cr\:LiSAF\)\. Focusing by a 1\-m lens to 0\.3\-1\.0 mm diameter \(1/e^2 intensity; typically 0\.5 mm\), the spot measured on a CCD from a 4\:1 image of a 4 % reflection at the sample plane, \>= 98 % Gaussian\. Damage criterion\: 'any visible permanent modification to the surface observable with the Nomarski microscope' after typically 600 shots at 10 Hz per site, 15\-30 fluence levels per pulse width \(pp\. 1750\-1751\)\. Plus a kinetic \(Fokker\-Planck\) and rate\-equation model of multiphoton\-seeded avalanche ionization in fused silica \(Sec\. IV\)\.

**Materials in structured entries:** BaF2, CaF2, LiF, MgF2, NaCl, SiO2

**Dataset quantities:** avalanche\_coefficient, band\_gap, damage\_threshold\_fluence, effective\_mass, multiphoton\_ionization\_cross\_section

**Contents:** 9 datasets; 7 formulas.

Curation notes
--------------

Journal pages 1749\-1761 = PDF pages 1\-13\. The PDF prints no DOI; identity from the library's bibliographic search, and title, authors and journal were checked against page 1\.

UNCERTAINTY \(p\. 1750\)\: 'Our estimated absolute uncertainty in fluence was 15%, but relative values when changing the laser pulse width or spot size are accurate to 5%\.' Level not stated\. The fluence is 'the effective diameter, as measured on the camera system, \.\.\. combined with the measured energy'; whether peak or average fluence is not said\. 'With short \(0\.4\-ps\) pulses, damage always occurred at the location corresponding to the peak of the Gaussian spatial profile' \(p\. 1751\)\. Short\-pulse thresholds are sharp\: 2 % below threshold, 10 000 pulses at 0\.4 ps produced no damage \(p\. 1752\)\.

SAMPLES\. Fused silica\: 1\-cm\-thick 'superpolished' Corning 7940, \< 1 nm rms roughness; a thin fused\-silica etalon gave the same thresholds \(p\. 1751\)\. Fluorides\: BaF2, CaF2, MgF2, LiF \(grades, orientation and polishing not stated beyond 'scratches left from the polishing process', p\. 1752\)\.

TEXT VALUES TAKEN \(p\. 1752\)\: 'Our measured short\-pulse \(0\.4 ps\) damage thresholds of BaF2 \(1\.6 J/cm2\), CaF2 \(2\.0 J/cm2\), MgF2 \(2\.1 J/cm2\), and LiF \(2\.6 J/cm2\) scale with band\-gap energy' \(the OCR of the library text drops the '2' of J/cm2; the pdf text layer confirms the values\)\. The wavelength is not named in the sentence\: 0\.4 ps is the shortest 1053\-nm pulse \(the 1053\-nm compressor gives 0\.4 ps \- 1 ns, p\. 1750; the 526\-nm pulses start at 275 fs\), and Fig\. 7 \(CaF2\) covers 0\.4\-1000 ps, the 1053\-nm range; so 1053 nm is recorded\.

FIGURES ONLY \(not digitised\)\. Fig\. 3\: fused\-silica damage fluence \(1\-50 J/cm2, log\) against pulse width \(0\.1\-1000 ps, log\) at 1053 nm \(about 2 J/cm2 at 0\.4 ps rising to about 40 J/cm2 at 900 ps\), a single 825\-nm point at 140 fs with a large error bar, and the tau^1/2 line; above 20 ps the data 'fit well to a tau^1/2 dependence \(actual fit\: tau^0\.504\)' \(p\. 1751\)\. Fig\. 6\: fused silica at 1053 nm \(0\.4\-60 ps\) and 526 nm \(0\.275\-7 ps, about 1\-2\.5 J/cm2\), measured points and the calculated curves of the model \(0\.01\-100 ps, 0\.3\-10 J/cm2\), and the calculated multiphoton\-ionization\-only limit at 1053 nm\. Fig\. 7\: CaF2 at 1053 nm, 0\.4\-1000 ps, 2\-25 J/cm2\. Figs\. 9\-18\: the model's conductivity, avalanche rate against intensity \(Fig\. 11\), electron densities, reflection and energy deposition\.

MODEL INPUTS \(fused silica; recorded as assumed datasets or in the formulas\)\: 'We assumed m\* = m\_e, U\_I = 9 eV, and the characteristic phonon energy, U\_phon was taken as 0\.033 eV' \(pp\. 1754\-1755\), with the electron scattering rates of Arnold, Cartier and DiMaria \(ref\. 28, Phys\. Rev\. A 45, 1477 \(1992\)\)\. The phonon energy has no quantity in the vocabulary\. The impact\-ionization rate 'was taken in the Keldysh impact ionization form \(ref\. 37, Ridley\) as 1\.5 \(epsilon/U\_I \- 1\)^2 fs^\-1' \(p\. 1753\)\. Four\-photon ionization at 526 nm\: 'We used the cross section sigma\_4 = 2 x 10^\-114 cm^8 sec^3\. This was measured for NaCl, but other insulators have nearly the same value \(ref\. 13\)' \(p\. 1756\); N\_s, 'the solid atom density', is given no value\. Eight\-photon ionization at 1053 nm is the fit Eq\. \(20\) to the Keldysh rate\. Damage criterion of the model\: the critical density ~1e21 cm^\-3 at 1053 nm; with 1e19 cm^\-3 instead the threshold 'would decrease by approximately 20%' \(p\. 1752\)\.

MODEL RESULTS\. The avalanche coefficient alpha \(beta = alpha I\)\: flux\-doubling estimate 'between 0\.0065 and 0\.013 cm2/ps GW' at 1053 nm, '1/alpha lies between 0\.08 and 0\.16 J/cm2' \(p\. 1755\); the numerical kinetic solution gives 0\.011 cm2/ps GW at 1053 nm \(p\. 1756, Fig\. 11\) and 0\.013 at 526 nm \(p\. 1757; the library text reads 'cm/ps GW', the pdf text layer 'cm2/ps GW'\); the scale fluence 2/alpha is 0\.2 J/cm2 \(1053 nm\) and 0\.15 J/cm2 \(526 nm\)\. Other model numbers \(notes only\)\: I\_b ~ 80 GW/cm2, tau\_b ~ 60 ps; p = 0\.85 in Eq\. \(A6\); sigma\_max E^2 = U\_I nu\_i\(1\.5 U\_I\) near 10 TW/cm2; seed concentrations below ~1e17 cm^\-3 unimportant at 10 TW/cm2; the 1e8 cm^\-3 'lucky electrons' matter only above ~5 ps; the plasma threshold of the 166\-fs calculation is ~1\.5 J/cm2 \(Figs\. 16\-18\)\.

REPRODUCED BY\: schaffer\_2001 \(Stuart's 526/1053 nm factor\-two statement\), jing\_2012 \(alpha ~ 0\.01 cm2 ps^\-1/GW\), mao\_2004 \(Fig\. 11 threshold marker, from Stuart ref\. 19\)\. Not in the library\: Stuart et al\., Phys\. Rev\. Lett\. 74, 2248 \(1995\) \(ref\. 24\) and J\. Opt\. Soc\. Am\. B 13, 459 \(1996\) \(cited by the others\); Jones et al\., Opt\. Eng\. 28, 1039 \(1989\) \(ref\. 13\)\. Du et al\., Appl\. Phys\. Lett\. 64, 3071 \(1994\) \(ref\. 23\) is du\_1994 \(its thresholds are figures only\)\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

stuart\_1996/damage\_BaF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "damage_BaF2",
     "material": "BaF2",
     "table": "text",
     "quantity": "damage_threshold_fluence",
     "unit": "J/cm2",
     "abscissa": "duration",
     "abscissa_unit": "ps",
     "use": "primary",
     "uncertainty": {
       "relative": 0.15,
       "level": "not stated"
     },
     "parameters": {
       "site": "surface",
       "criterion": "any visible permanent modification of the front surface under a Nomarski microscope",
       "shots": 600,
       "wavelength_nm": 1053
     }
   }

1 inline points in the source record.

p\. 1752, 'short\-pulse \(0\.4 ps\) damage threshold'\. Wavelength 1053 nm inferred as explained in the source notes\. 15 % absolute uncertainty \(p\. 1750\), level not stated\.

stuart\_1996/damage\_CaF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "damage_CaF2",
     "material": "CaF2",
     "table": "text",
     "quantity": "damage_threshold_fluence",
     "unit": "J/cm2",
     "abscissa": "duration",
     "abscissa_unit": "ps",
     "use": "primary",
     "uncertainty": {
       "relative": 0.15,
       "level": "not stated"
     },
     "parameters": {
       "site": "surface",
       "criterion": "any visible permanent modification of the front surface under a Nomarski microscope",
       "shots": 600,
       "wavelength_nm": 1053
     }
   }

1 inline points in the source record.

p\. 1752, as for BaF2\. Fig\. 7 shows the CaF2 threshold from 0\.4 to 1000 ps \(figure only\)\.

stuart\_1996/damage\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "damage_MgF2",
     "material": "MgF2",
     "table": "text",
     "quantity": "damage_threshold_fluence",
     "unit": "J/cm2",
     "abscissa": "duration",
     "abscissa_unit": "ps",
     "use": "primary",
     "uncertainty": {
       "relative": 0.15,
       "level": "not stated"
     },
     "parameters": {
       "site": "surface",
       "criterion": "any visible permanent modification of the front surface under a Nomarski microscope",
       "shots": 600,
       "wavelength_nm": 1053
     }
   }

1 inline points in the source record.

p\. 1752, as for BaF2\. The crystal orientation and polarization relative to the axis are not stated\.

stuart\_1996/damage\_LiF
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "damage_LiF",
     "material": "LiF",
     "table": "text",
     "quantity": "damage_threshold_fluence",
     "unit": "J/cm2",
     "abscissa": "duration",
     "abscissa_unit": "ps",
     "use": "primary",
     "uncertainty": {
       "relative": 0.15,
       "level": "not stated"
     },
     "parameters": {
       "site": "surface",
       "criterion": "any visible permanent modification of the front surface under a Nomarski microscope",
       "shots": 600,
       "wavelength_nm": 1053
     }
   }

1 inline points in the source record.

p\. 1752, as for BaF2\.

stuart\_1996/model\_band\_gap
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "model_band_gap",
     "material": "SiO2",
     "table": "text",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

1 inline points in the source record.

Model input\: 'We assumed m\* = m\_e, U\_I = 9 eV, and the characteristic phonon energy, U\_phon was taken as 0\.033 eV' \(pp\. 1754\-1755\)\. No source is cited for U\_I\.

stuart\_1996/model\_effective\_mass
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "model_effective_mass",
     "material": "SiO2",
     "table": "text",
     "quantity": "effective_mass",
     "unit": "m_e",
     "abscissa": "none",
     "use": "check",
     "parameters": {
       "carrier": "electron",
       "assumed": true
     }
   }

1 inline points in the source record.

Model input for the conduction electrons of the kinetic equation, 'We assumed m\* = m\_e' \(p\. 1754\)\. The mass enters the conductivity per electron, Eq\. \(4\); the scattering rates are Arnold, Cartier and DiMaria's \(ref\. 28\)\.

stuart\_1996/model\_sigma4
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "model_sigma4",
     "material": "SiO2",
     "table": "text",
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm8 s3",
     "abscissa_unit": "nm",
     "use": "check",
     "reproduced_from": [
       "S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen and P. Kelly, Opt. Eng. 28, 1039 (1989)"
     ],
     "parameters": {
       "photons": 4,
       "assumed": true
     }
   }

1 inline points in the source record.

Model input for fused silica at 526 nm, Eq\. \(19\) P\(I\) = sigma\_4 \(I/hbar omega\)^4 N\_s\: 'We used the cross section sigma\_4 = 2 x 10^\-114 cm^8 sec^3\. This was measured for NaCl, but other insulators have nearly the same value \(ref\. 13\)' \(p\. 1756\)\. The NaCl value itself is the dataset sigma4\_NaCl\.

stuart\_1996/sigma4\_NaCl
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma4_NaCl",
     "material": "NaCl",
     "table": "text",
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm8 s3",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen and P. Kelly, Opt. Eng. 28, 1039 (1989)"
     ],
     "parameters": {
       "photons": 4
     }
   }

1 inline points in the source record.

p\. 1756\: the four\-photon cross section 'measured for NaCl' \(ref\. 13\), quoted as the value used at 526 nm\. The wavelength of the NaCl measurement is not stated here; 526 nm is the wavelength at which Stuart et al\. apply it \(Jones et al\. is not in the library to check\)\.

stuart\_1996/model\_avalanche\_coefficient
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "model_avalanche_coefficient",
     "material": "SiO2",
     "table": "text",
     "quantity": "avalanche_coefficient",
     "unit": "cm2/(ps GW)",
     "abscissa_unit": "nm",
     "use": "check",
     "parameters": {
       "definition": "alpha in dn/dt = alpha I(t) n (Eq. 18), from the kinetic (Fokker-Planck) equation of Sec. IV"
     }
   }

2 inline points in the source record.

Calculated, not measured\: the avalanche coefficient alpha of beta = alpha I \(Eqs\. 16, 18\) from the numerical solution of the kinetic equation, 'From the figure, alpha = 0\.011 cm2/ps GW' at 1053 nm \(p\. 1756, Fig\. 11\) and 'alpha = 0\.013 cm2/ps GW \.\.\. for fused silica at 526 nm' \(p\. 1757\)\. The flux\-doubling estimate at 1053 nm is 0\.0065\-0\.013 \(p\. 1755\)\. Inputs\: U\_I = 9 eV, m\* = m\_e, U\_phon = 0\.033 eV and Arnold et al\.'s scattering rates\. Checked\: 2/alpha = 0\.18 J/cm2 at 1053 nm \(printed 'the scale fluence 2/alpha is 0\.2 J/cm2'\) and 0\.154 at 526 nm \(printed 0\.15\)\.

Formulas
--------

stuart\_1996/kinetic\_equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kinetic_equation",
     "material": "SiO2",
     "equation": "Eqs. (1)-(6), pp. 1753-1754",
     "printed": "df/dt + d/de [V(e) f - D(e) df/de] = S(e,t); V(e) = sigma(e) E^2(t)/3 - U_phon gamma(e); D(e) = 2 sigma(e) E^2 e / 3; sigma(e) = e^2 tau_m(e) / (m* [1 + omega^2 tau_m^2(e)]); S = R_imp + R_pi; R_imp(e,t) = -nu_i(e) f(e) + 4 nu_i(2e + U_I) f(2e + U_I)",
     "variable": "e (epsilon): electron kinetic energy in the conduction band; f(e,t) de the electron density with energy e; E the laser field; tau_m(e) the momentum scattering time; gamma(e) the energy-transfer rate to the lattice",
     "coefficients": {
       "m_star": "m_e",
       "U_I": "9 eV",
       "U_phon": "0.033 eV"
     },
     "check": "Not reproduced numerically: tau_m(e) and gamma(e) are Arnold, Cartier and DiMaria's (ref. 28) and are shown only in Fig. 9."
   }

Fokker\-Planck equation for the electron energy distribution \(refs\. 3, 10\)\. Boundary conditions\: the distribution vanishes at infinite energy and the current at zero energy\. The flux\-doubling alternative replaces R\_imp by f\(U\_I,t\) = 0, J\(0,t\) = 2 J\(U\_I,t\) \(Eq\. 7\), valid when U\_I nu\_i\(2e \+ U\_I\) \>\> sigma\_max E^2 \(Eq\. 8\)\.

stuart\_1996/impact\_ionization\_rate
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "impact_ionization_rate",
     "material": "SiO2",
     "equation": "p. 1753 (text after Eq. 6)",
     "printed": "nu_i(e) = 1.5 (e/U_I - 1)^2 fs^-1",
     "variable": "e: electron kinetic energy; U_I = 9 eV the band gap",
     "coefficients": {
       "prefactor": "1.5 fs^-1",
       "U_I": "9 eV"
     },
     "reproduced_from": [
       "B. K. Ridley, Quantum Processes in Semiconductors (Clarendon, Oxford, 1993), pp. 276-278"
     ],
     "check": "Nothing printed to reproduce."
   }

'The ionization rate nu\_i\(e\) was taken in the Keldysh impact ionization form \(ref\. 37\) as 1\.5 \(e/U\_I \- 1\)^2 fs^\-1' \(p\. 1753\); zero below U\_I is implied, not stated\.

stuart\_1996/avalanche\_rate
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "avalanche_rate",
     "material": "SiO2",
     "equation": "Eq. (16), p. 1755, and Eq. (A6), p. 1760",
     "printed": "beta = p E^2 / int_0^U_I de/sigma(e) = alpha I",
     "variable": "E: laser field; I the intensity; p a numerical factor between 0.5 and 1.0 (the numerical calculations give p = 0.85, p. 1760)",
     "coefficients": {
       "p": "0.5-1.0 (numerically 0.85)"
     },
     "check": "The flux-doubling range 0.0065-0.013 cm2/(ps GW) gives 1/alpha = 0.077-0.154 J/cm2, the printed 'between 0.08 and 0.16 J/cm2' (checked 2026-09-26)."
   }

Valid for I \>\> I\_b ~ 80 GW/cm2 \(p\. 1754\)\. See the dataset model\_avalanche\_coefficient\.

stuart\_1996/mpi\_526nm
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "mpi_526nm",
     "material": "SiO2",
     "equation": "Eq. (19), p. 1756",
     "printed": "P(I) = sigma_4 (I/hbar omega)^4 N_s, sigma_4 = 2 x 10^-114 cm^8 sec^3",
     "variable": "I: intensity; hbar omega the 526-nm photon energy; N_s 'the solid atom density' (no value given)",
     "coefficients": {
       "sigma_4": "2e-114 cm^8 s^3"
     },
     "reproduced_from": [
       "S. C. Jones, P. Braunlich, R. T. Casper, X.-A. Shen and P. Kelly, Opt. Eng. 28, 1039 (1989)"
     ],
     "check": "Not reproducible without N_s."
   }

The four\-photon cross section of NaCl, applied to fused silica \(see model\_sigma4\)\.

stuart\_1996/mpi\_1053nm\_fit
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "mpi_1053nm_fit",
     "material": "SiO2",
     "equation": "Eq. (20), p. 1756",
     "printed": "P(I) = 9.52 x 10^10 I^8 cm^-3 ps^-1, where the intensity I is in TW/cm^2",
     "variable": "I: intensity in TW/cm2 at 1053 nm",
     "coefficients": {
       "prefactor": "9.52e10 cm^-3 ps^-1 (TW/cm^2)^-8"
     },
     "check": "A fit to the Keldysh rate (ref. 38) for fused silica with U_I = 9 eV, 'valid up to intensities on the order of 10^3 TW/cm^2'; the Keldysh evaluation itself is not printed, so not reproduced."
   }

'For 1053\-nm light, eight\-photon absorption cross\-section values were not available, so we used the strong\-field Keldysh formula for P\(I\)\. Evaluation of the Keldysh expression leads to a result that is fit very well by the eight\-photon absorption form' \(p\. 1756\)\.

stuart\_1996/rate\_equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "rate_equation",
     "material": "SiO2",
     "equation": "Eqs. (18), (21), (23)-(26), pp. 1756-1757",
     "printed": "dn/dt = beta(I) n + P(I) (21); n = n_0 exp[alpha I_0 tau (pi/ln 2)^(1/2) / 4] (23); F_cr = (I_0 tau/2)(pi/ln 2)^(1/2) = (2/alpha) ln(n_cr/n_0) (25); Phi_cr = tau^(3/4) (n_cr/(sigma_4 N_s))^(1/4) (pi/ln 2)^(3/8) hbar omega / sqrt(2) (26)",
     "variable": "I(t) = I_0 exp(-4 ln 2 t^2/tau^2), tau the intensity FWHM (Eq. 22); n_0 the multiphoton-produced density (Eq. 24); n_cr the critical density",
     "coefficients": {
       "n_cr": "~1e21 cm^-3 (1053 nm)"
     },
     "check": "2/alpha from alpha = 0.011 (0.013) cm2/(ps GW) is 0.18 (0.154) J/cm2, printed 0.2 (0.15) J/cm2 (checked 2026-09-26)."
   }

The analytic estimate separating multiphoton seeding at the pulse peak from the avalanche; Eq\. \(26\) is the multiphoton\-only limit for four\-photon absorption, scaling generally as tau^\(\(m\-1\)/m\) n\_cr^\(1/m\)\.

stuart\_1996/plasma\_absorption
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "plasma_absorption",
     "material": "SiO2",
     "equation": "Eqs. (33)-(35), pp. 1758",
     "printed": "a = alpha n [<e> + U_I] (33); epsilon(omega) = 1 - n <sigma>(i + omega tau_m)/omega = 1 - (n/n_c) / (1 + i/(omega tau_m)) (34); T = |2 Re sqrt(epsilon) / (1 + sqrt(epsilon))|^2 (35)",
     "variable": "a: intensity absorption coefficient; n the electron density; <e> the mean electron energy",
     "coefficients": {
       "alpha_inverse": "0.1 J/cm^2",
       "energy": "<e> + U_I = 15 eV"
     },
     "check": "With 1/alpha = 0.1 J/cm2, <e> + U_I = 15 eV and n_cr = 1e21 cm^-3, Eq. (33) gives a = 2.403 um^-1 (n/n_cr); printed 'a = 2.4 (n/n_cr) um^-1' (checked 2026-09-26)."
   }

The Drude response of the conduction electrons \(p\. 1758\)\.

Corrections
-----------

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.